- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

One-dimensional reduction of the three-dimenstional Gross-Pitaevskii equation with two- and three-body interactions

W. B. Cardoso1, A. T. Avelar1, and D. Bazeia2

  • 1Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia, Goiás, Brazil
  • 2Departamento de Física, Universidade Federal da Paraíba, 58051-970, João Pessoa, Paraíba, Brazil

PDF

Phys. Rev. E 83, 036604 – Published 17 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036604

Abstract

We deal with the three-dimensional Gross-Pitaevskii equation which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation,controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.

View figure in article

Article Text

References (37)

  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
  2. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
  3. C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002).
  4. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003).
  5. S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G. V. Shlyapnikov, and M. Lewenstein, Phys. Rev. Lett. 83, 5198 (1999).
  6. J. Denschlag, J. E. Simsarian, D. L. Feder, Charles W. Clark, L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley, K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. D. Phillips, Science 287, 97 (2000).
  7. K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, Nature (London) 417, 150 (2002).
  8. L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, Science 296, 1290 (2002).
  9. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003).
  10. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
  11. A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001).
  12. B. A. Malomed, Soliton Management in Periodic Systems (Springer, New York, 2006).
  13. J. L. Roberts, N. R. Claussen, S. L. Cornish, E. A. Donley, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 86, 4211 (2001).
  14. S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, Nature (London) 392, 151 (1998).
  15. E. Timmermans, P. Tommasini, M. Hussein, and A. Kerman, Phys. Rep. 315, 199 (1999).
  16. P. G. Kevrekidis, G. Theocharis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Rev. Lett. 90, 230401 (2003).
  17. F. Kh. Abdullaev and V. V. Konotop, Nonlinear Waves: Classical and Quantum Aspects (Kluwer Academic, New York, 2004), p. 251.
  18. V. M. Pérez-García, H. Michinel, and H. Herrero, Phys. Rev. A 57, 3837 (1998).
  19. A. D. Jackson, G. M. Kavoulakis, and C. J. Pethick, Phys. Rev. A 58, 2417 (1998).
  20. L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A 65, 043614 (2002).
  21. L. Salasnich, Laser Phys. 12, 198 (2002).
  22. L. Salasnich, A. Cetoli, B. A. Malomed, F. Toigo, and L. Reatto, Phys. Rev. A 76, 013623 (2007).
  23. S. K. Adhikari and L. Salasnich, New J. Phys. 11, 023011 (2009).
  24. L. Salasnich and B. A. Malomed, Phys. Rev. A 79, 053620 (2009).
  25. L. Salasnich, J. Phys. A: Math. Theor. 42, 335205 (2009).
  26. G. Filatrella, B. A. Malomed, and L. Salasnich, Phys. Rev. A 79, 045602 (2009).
  27. G. Gligorić, A. Maluckov, L. Salasnich, B. A. Malomed, and Lj. Hadžievski, Chaos 19, 043105 (2009).
  28. L. E. Young-S, L. Salasnich, and S. K. Adhikari, Phys. Rev. A 82, 053601 (2010).
  29. T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch, A. Jaakkola, H.-C. Nägerl, and R. Grimm, Nature (London) 440, 315 (2006).
  30. G. Roati, M. Zaccanti, C. D’Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, Phys. Rev. Lett. 99, 010403 (2007).
  31. L. Mazza, M. Rizzi, M. Lewenstein, and J. I. Cirac, Phys. Rev. A 82, 043629 (2010).
  32. Y. Wang, J. P. D’Incao, and B. D. Esry, e-print arXiv:0906.5019.
  33. A. T. Avelar, D. Bazeia, and W. B. Cardoso, Phys. Rev. E 79, 025602(R) (2009).
  34. W. B. Cardoso, A. T. Avelar, and D. Bazeia, Nonlinear Anal. Real World Appl. 11, 4269 (2010).
  35. C. Chin, T. Kraemer, M. Mark, J. Herbig, P. Waldburger, H.-C. Nägerl, and R. Grimm, Phys. Rev. Lett. 94, 123201 (2005).
  36. F. Kh. Abdullaev, A. Gammal, L. Tomio, and T. Frederico, Phys. Rev. A 63, 043604 (2001); A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002); A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, ibid. 89, 040401 (2002); P. Pieri and G. C. Strinati, ibid. 91, 030401 (2003); T. Köhler, ibid. 89, 210404 (2002); A.-X. Zhang and J.-K. Xue, Phys. Rev. A 75, 013624 (2007); U. Roy, R. Atre, C. Sudheesh, C. N. Kumar, and P. K. Panigrahi, J. Phys. B: At. Mol. Opt. Phys. 43, 025003 (2010).
  37. P. Muruganandam and S. K. Adhikari, Comput. Phys. Commun. 180, 1888 (2009).

Outline

Information

Phys. Rev. E 83, 036604– Published 17 March, 2011
  • Received 8 December 2010

©2011 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation